A low-noise series-array Josephson junction parametric amplifier

We have obtained parametric gain at 19 GHz from a distributed Josephson junction parametric amplifier whose active gain medium consists of a series array of 1000 Josephson junctions embedded in a coplanar waveguide. When cooled to 1.7 K the amplifier provides 16 dB gain in a mode where the internally generated double sideband noise referred to input is 0.5 ± 0.1 K. This noise is consistent with Nyquist noise generated from the losses. An instantaneous bandwidth of 125 MHz has been observed with a peak gain of 12 dB. The 3 dB compression point with a peak gain of 14.6 dB is -90.5 dB and the dynamic range is 38 dB

Experimental Measurement of the Persistence Exponent of the Planar Ising Model

Using a twisted nematic liquid crystal system exhibiting planar Ising model dynamics, we have measured the scaling exponent $\theta$ which characterizes the time evolution, $p(t) \sim t^{-\theta}$, of the probability p(t) that the local order parameter has not switched its state by the time t. For 0.4 seconds to 200 seconds following the phase quench, the system exhibits scaling behavior and, measured over this interval, $\theta = 0.19 \pm 0.031$, in good agreement with theoretical analysis and numerical simulations.Comment: 4 pages RevTeX (multicol.sty and epsf.sty needed): 1 EPS figure. Introduction and reference list modifie

Phase ordering in bulk uniaxial nematic liquid crystals

The phase-ordering kinetics of a bulk uniaxial nematic liquid crystal is addressed using techniques that have been successfully applied to describe ordering in the O(n) model. The method involves constructing an appropriate mapping between the order-parameter tensor and a Gaussian auxiliary field. The mapping accounts both for the geometry of the director about the dominant charge 1/2 string defects and biaxiality near the string cores. At late-times t following a quench, there exists a scaling regime where the bulk nematic liquid crystal and the three-dimensional O(2) model are found to be isomorphic, within the Gaussian approximation. As a consequence, the scaling function for order-parameter correlations in the nematic liquid crystal is exactly that of the O(2) model, and the length characteristic of the strings grows as $t^{1/2}$. These results are in accord with experiment and simulation. Related models dealing with thin films and monopole defects in the bulk are presented and discussed.Comment: 21 pages, 3 figures, REVTeX, submitted to Phys. Rev.

Phase Ordering of 2D XY Systems Below T_{KT}

We consider quenches in non-conserved two-dimensional XY systems between any two temperatures below the Kosterlitz-Thouless transition. The evolving systems are defect free at coarse-grained scales, and can be exactly treated. Correlations scale with a characteristic length $L(t) \propto t^{1/2}$ at late times. The autocorrelation decay exponent, $\bar{\lambda} = (\eta_i+\eta_f)/2$, depends on both the initial and the final state of the quench through the respective decay exponents of equilibrium correlations, $C_{EQ}(r) \sim r^{-\eta}$. We also discuss time-dependent quenches.Comment: LATeX 11 pages (REVTeX macros), no figure

Hydrodynamics of topological defects in nematic liquid crystals

We show that back-flow, the coupling between the order parameter and the velocity fields, has a significant effect on the motion of defects in nematic liquid crystals. In particular the defect speed can depend strongly on the topological strength in two dimensions and on the sense of rotation of the director about the core in three dimensions.Comment: 4 pages including two figure

Phase Ordering Kinetics with External Fields and Biased Initial Conditions

The late-time phase-ordering kinetics of the O(n) model for a non-conserved order parameter are considered for the case where the O(n) symmetry is broken by the initial conditions or by an external field. An approximate theoretical approach, based on a `gaussian closure' scheme, is developed, and results are obtained for the time-dependence of the mean order parameter, the pair correlation function, the autocorrelation function, and the density of topological defects [e.g. domain walls ($n=1$), or vortices ($n=2$)]. The results are in qualitative agreement with experiments on nematic films and related numerical simulations on the two-dimensional XY model with biased initial conditions.Comment: 35 pages, latex, no figure

Hydrodynamics of domain growth in nematic liquid crystals

We study the growth of aligned domains in nematic liquid crystals. Results are obtained solving the Beris-Edwards equations of motion using the lattice Boltzmann approach. Spatial anisotropy in the domain growth is shown to be a consequence of the flow induced by the changing order parameter field (backflow). The generalization of the results to the growth of a cylindrical domain, which involves the dynamics of a defect ring, is discussed.Comment: 12 revtex-style pages, including 12 figures; small changes before publicatio

Vortex Velocity Pair Correlations

The vortex velocity probability distribution for two distinct vortices is determined for the case of phase-ordering kinetics in systems with point defects. The n-vector model driven by time-dependent Ginzburg-Landau dynamics for a nonconserved order parameter is considered. The description includes the effects of other vortices and order parameter fluctuations. At short distances the most probable configuration is that a vortex-antivortex pair have only a nonzero relative velocity which is inversely proportional to the distance between them. The coefficient of proportionality is determined explicitly.Comment: 51 pages, 4 figure

Growth Laws for Phase Ordering

We determine the characteristic length scale, $L(t)$, in phase ordering kinetics for both scalar and vector fields, with either short- or long-range interactions, and with or without conservation laws. We obtain $L(t)$ consistently by comparing the global rate of energy change to the energy dissipation from the local evolution of the order parameter. We derive growth laws for O(n) models, and our results can be applied to other systems with similar defect structures.Comment: 12 pages, LaTeX, second tr

Phase-ordering dynamics of the Gay-Berne nematic liquid crystal

Phase-ordering dynamics in nematic liquid crystals has been the subject of much active investigation in recent years in theory, experiments and simulations. With a rapid quench from the isotropic to nematic phase a large number of topological defects are formed and dominate the subsequent equilibration process. We present here the results of a molecular dynamics simulation of the Gay-Berne model of liquid crystals after such a quench in a system with 65536 molecules. Twist disclination lines as well as type-1 lines and monopoles were observed. Evidence of dynamical scaling was found in the behavior of the spatial correlation function and the density of disclination lines. However, the behavior of the structure factor provides a more sensitive measure of scaling, and we observed a crossover from a defect dominated regime at small values of the wavevector to a thermal fluctuation dominated regime at large wavevector.Comment: 18 pages, 16 figures, animations available at http://www.physics.brown.edu/Users/faculty/pelcovits/lc/coarsening.htm